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A221993
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Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..2 array extended with zeros and convolved with 1,4,6,4,1.
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1
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2, 3, 4, 6, 10, 15, 22, 36, 56, 84, 133, 208, 318, 495, 772, 1192, 1846, 2870, 4448, 6886, 10686, 16576, 25679, 39819, 61763, 95732, 148415, 230158, 356829, 553197, 857766, 1329946, 2061917, 3196940, 4956807, 7685148, 11915388, 18474452, 28643620
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = a(n-1) + 3*a(n-3) - 2*a(n-4) - 3*a(n-6) + 2*a(n-7) + a(n-9).
Empirical g.f.: x*(1 + x + x^2)*(2 - x - 3*x^3 + 2*x^4 + x^6) / (1 - x - 3*x^3 + 2*x^4 + 3*x^6 - 2*x^7 - x^9). - Colin Barker, Aug 14 2018
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EXAMPLE
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Some solutions for n=7, one extended zero followed by filtered positions:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....1....1....0....0....1....1....0....1....0....0....0....1
..1....0....0....1....0....0....0....1....0....0....1....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....1....1....0....0
..0....1....0....1....0....0....0....0....1....0....0....0....0....0....0....1
..0....0....1....0....0....0....0....0....0....1....0....0....1....0....0....0
..0....1....0....0....1....0....1....1....0....0....0....0....0....1....0....0
..0....0....0....0....0....0....0....0....0....0....1....1....0....0....0....1
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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